A nonzero polynomial with rational coefficients has all of the numbers [1 sqrt{2}, ; 2 sqrt{3}, ;3 sqrt{4},; dots, ;1000 sqrt{10
1 answer:
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Assuming the equation is:
When fractions involve numeric denominators, the fractions can be removed by multiplying (both sides) by the LCM of the denominators.
Here the denominators are 2 and 10, hence the LCM is 10.
Multiply by 10 on both sides, not forgetting to distribute when multiplying on the right side:
simplify, remember that there are always implied parentheses around numerators and denominators:
Now, distribute, i.e. remove parentheses and distribute:
5x-10x+25=30x+90-10x+140
Simplify
-5x+25=20x+230
transpose terms
25-230=20x+5x
solve
x=-205/25=-41/5
In this particular case, we can also take advantage of the term
(10x-25)/10=5(2x-5)/10=(2x-5)/2 which greatly simplifies the solution process, because the LCM will then be 2 instead of 10.
If we do that, the solution will be:
Multiply by 2 on both sides, not forgetting to distribute when multiplying on the right side:
simplify, remember that there are always implied parentheses around numerators and denominators:
Now, distribute, i.e. remove parentheses and distribute:
Simplify
-x+5=4x+46
solve
5-46=4x+x
-41=5x
x=-41/5
with the same results.